Solve sqrt{{left(3sqrt{2}right)}^2+{left(3sqrt{2}right)}^2}

$$\sqrt{ { \left(3 \sqrt{ 2 } \right) }^{ 2 } + { \left(3 \sqrt{ 2 } \right) }^{ 2 } }$$

Evaluate

$$6$$

Solution Steps

Expand \left(3\sqrt{2}\right)^{2}.

$$\sqrt{3^{2}\left(\sqrt{2}\right)^{2}+\left(3\sqrt{2}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9\left(\sqrt{2}\right)^{2}+\left(3\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{9\times 2+\left(3\sqrt{2}\right)^{2}}$$

Multiply 9 and 2 to get 18.

$$\sqrt{18+\left(3\sqrt{2}\right)^{2}}$$

Expand \left(3\sqrt{2}\right)^{2}.

$$\sqrt{18+3^{2}\left(\sqrt{2}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{18+9\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{18+9\times 2}$$

Multiply 9 and 2 to get 18.

$$\sqrt{18+18}$$

Add 18 and 18 to get 36.

$$\sqrt{36}$$

Calculate the square root of 36 and get 6.

$$6$$

Factor

$$2\times 3$$